Vol. 27, No. 3, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Sequences of contractions and fixed points

Sam Bernard Nadler, Jr.

Vol. 27 (1968), No. 3, 579–585
Abstract

Given a convergent sequence of contraction mappings, the convergence of the sequence of their fixed points is investigated in §1 of this paper. The results obtained lead to a necessary and sufficient condition in order that a separable or a reflexive Banach space be finite dimensional. An application to differential equations is also included.

In §2 we consider mappings defined on the cartesian product of two metric spaces which are contraction mappings in one variable or in each variable separately. Using some of the results of §1 we prove that, with certain restrictions, such mappings have fixed point.

Mathematical Subject Classification
Primary: 54.85
Secondary: 34.00
Milestones
Received: 9 February 1968
Revised: 22 March 1968
Published: 1 December 1968
Authors
Sam Bernard Nadler, Jr.